Holographic quantum dynamics simulation

ABSTRACT

A quantum computer controller receives a quantum circuit comprising circuit slices. The first slice comprises a past causal cone of a first system qubit wire at a fully evolved level of the circuit. An i-th slice contains all gates that are within a past causal cone of a system qubit wire that reaches the fully evolved level in slice i that are not in the past causal cone of a system qubit wire that reaches the fully evolved level in slice i−j. The controller causes execution of the i-th slice using the physical qubits; causes a physical qubit that was evolved along a system qubit wire to the fully evolved level via execution of the i-th slice to be reinitialized and reintroduced onto a system qubit wire at a base level of the i+m-th slice; and causes the quantum computer to use the physical qubit to execute the i+m-th slice.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.16/705,727, filed Dec. 6, 2019, the content of which is herebyincorporated by reference in its entirety.

TECHNICAL FIELD

Various embodiments relate to the execution of a quantum circuit by aquantum computer. For example, various embodiments relate to theexecution of a quantum circuit by a quantum computer with efficientqubit usage.

BACKGROUND

Near-term quantum computing hardware will have access to only a limitednumber (10's to 100's) of quantum bits (qubits), and will also bestrongly limited by noise and gate errors. The relatively small numberof noisy qubits makes it difficult to effectively solve complex problemsthat are very challenging to solve using classical computing means.Through applied effort, ingenuity, and innovation many deficiencies ofsuch systems have been solved by developing solutions that arestructured in accordance with the embodiments of the present invention,many examples of which are described in detail herein.

BRIEF SUMMARY OF EXAMPLE EMBODIMENTS

Various embodiments provide methods, quantum computers, computingentities (e.g., classical computing entities), systems, computer programproducts, and/or the like. According to one aspect, a quantum computermay execute a quantum circuit via efficient use of the physical qubitsof the quantum computer. In an example embodiment, a controller of aquantum computer receives a quantum circuit comprising a plurality ofcircuit slices. The quantum computer comprises the controller, qubitmanagement systems, and a plurality of physical qubits. A first slice ofthe plurality of circuit slices comprises a past causal cone of a firstsystem qubit wire at a fully evolved level of the quantum circuit. Ani-th slice of the plurality of circuit slices is defined to contain allgates that are not within a past causal cone of any system qubit wire ofthe quantum circuit that reaches the fully evolved level of the quantumcircuit in slice i−j, where 0≤j<i is an integer, but that can now beexecuted by initiating one or more physical qubits that have reached thefully evolved level during execution of slice i−1, have optionally beenmeasured, and reset onto the system qubit wires in a base level of slicei. For example, an i-th slice may contain all gates that are within apast causal cone of a system qubit wire that reaches the fully evolvedlevel of the quantum circuit via execution of slice i that are not inthe past causal cone of a system qubit wire that reaches the fullyevolved level in slice i−j, where 0<j<i is an integer. The controllercauses execution of the i-th slice of the quantum circuit using thephysical qubits of the quantum computer; causes a physical qubit thatwas evolved as the system qubit fully evolved via execution of the i-thslice to be optionally measured, and reinitialized and reintroduced ontoa system qubit wire at a base level of the i+m-th slice, m a positiveinteger; and causes the quantum computer to use the physical qubit toexecute the i+m-th slice of the quantum circuit.

According to another aspect, a method is provided. In an exampleembodiment, the method comprises receiving, by a controller of a quantumcomputer, a quantum circuit comprising a plurality of circuit slices.The quantum computer comprises qubit management systems and a pluralityof physical qubits. A first slice of the plurality of circuit slicescomprises a past causal cone of a first system qubit wire at a fullyevolved level of the quantum circuit. An i-th slice of the quantumcircuit is defined to contain all gates that are not within a pastcausal cone of any system qubit wire of the quantum circuit that reachesthe fully evolved level of the quantum circuit in slice i−j, where 0<j<iis an integer, but that can now be executed by initiating one or morephysical qubits that have reached the fully evolved level duringexecution of slice i−1, have optionally been measured, and reset ontothe system qubit wires in a base level of slice i. The method furthercomprises causing, by the controller, execution of the i-th slice of thequantum circuit using the physical qubits of the quantum computer;causing, by the controller, a physical qubit that was evolved as thesystem qubit fully evolved via execution of the i-th slice to beoptionally measured, and reinitialized and reintroduced onto a systemqubit wire at a base level of the i+m-th slice, m a positive integer;and causing, by the controller, the quantum computer to use the physicalqubit to execute the i+m-th slice of the quantum circuit.

In an example embodiment, executing the i-th slice of the quantumcircuit comprises executing all gates for which incoming and outgoingwires lie within the i-th slice in order to propagate the system qubitsforward in time. In an example embodiment, the quantum circuit comprisesat least one ancilla wire and executing the i-th slice of the quantumcircuit comprises interacting one or more system qubits at a bottom ofthe i-th slice with at least one ancilla qubit via unitary gates inorder to introduce initial correlations between the one or more systemqubits at the bottom of the i-th slice and system qubits at the bottomof one or more other slices. In an example embodiment, the quantumcircuit encodes interactions governed by a Hamiltonian characterized bylocal interactions. In an example embodiment, system qubit wirecorresponds to a degree of freedom associated with a section of aphysical domain being simulated. In an example embodiment, executing thei-th slice of the quantum circuit comprises evolving the degree offreedom in accordance with an operator. In an example embodiment, theoperator is a Hamiltonian. In an example embodiment, the physical domainis one of a one dimensional, two dimensional, or three dimensionalphysical domain. In an example embodiment, the quantum circuit simulatesthe dynamics of the evolution of quantum states defined on a latticerepresenting the physical domain. In an example embodiment, the methodfurther comprises performing one or more measurements of at least onephysical qubit of the plurality of qubits to determine a valuecorresponding to at least one degree of freedom within the physicaldomain. In an example embodiment, at least one system qubit wire of thequantum circuit extends through multiple slices of quantum circuit.

According to yet another aspect, a computing entity is provided. In anexample embodiment, the computing entity is in communication with acontroller of a quantum computer. The quantum computer comprises qubitmanagement systems and a plurality of physical qubits. The computingentity is configured to cause the controller to control elements of thequantum computer to receive, by the controller, a quantum circuitcomprising a plurality of circuit slices. A first slice of the pluralityof circuit slices comprises a past causal cone of a first system qubitwire at a fully evolved level of the quantum circuit. An i-th slice ofthe plurality of circuit slices is defined to contain all gates that arenot within a past causal cone of any system qubit wires of the quantumcircuit that reach the fully evolved level of the quantum circuit inslice i−j, where 0<j<i is an integer, but that can now be executed byinitiating one or more physical qubits that have reached the fullyevolved level during execution of slice i−1, have optionally beenmeasured, and reset onto the system qubit wires in a base level of slicei. The computing entity is further configured to cause the controller tocontrol elements of the quantum computer to cause the quantum computerto execute of the i-th slice of the quantum circuit using the physicalqubits; cause the quantum computer to initialize a physical qubit, whichwas evolved along at least one system qubit wire to be fully evolved viaexecution of the i-th slice, onto a system qubit wire at a base level ofthe i+m-th slice of the quantum circuit, m a positive integer; and causethe quantum computer to use the physical qubit to execute the i+m-thslice of the quantum circuit.

In an example embodiment, executing the i-th slice of the quantumcircuit comprises executing all gates for which incoming and outgoingwires lie within the i-th slice in order to propagate the system qubitsforward in time. In an example embodiment, the quantum circuit comprisesat least one ancilla wire and executing the i-th slice of the quantumcircuit comprises interacting one or more system qubits at a bottom ofthe i-th slice with at least one ancilla qubit via unitary gates inorder to introduce initial correlations between the one or more systemqubits at the bottom of the i-th slice and system qubits at the bottomof one or more other slices. In an example embodiment, the quantumcircuit encodes interactions governed by a Hamiltonian characterized bylocal interactions. In an example embodiment, system qubit wirecorresponds to a degree of freedom associated with a section of aphysical domain being simulated. In an example embodiment, executing thei-th slice of the quantum circuit comprises evolving the degree offreedom in accordance with an operator. In an example embodiment, theoperator is a Hamiltonian. In an example embodiment, the physical domainis one of a one dimensional, two dimensional, or three dimensionalphysical domain. In an example embodiment, the quantum circuit simulatesthe dynamics of the evolution of quantum states defined on a latticerepresenting the physical domain. In an example embodiment, Thecomputing entity is further configured to cause the controller tocontrol elements of the quantum computer to cause the quantum computerto perform one or more measurements of at least one physical qubit ofthe plurality of qubits to determine a value corresponding to at leastone degree of freedom within the physical domain. In an exampleembodiment, at least one system qubit wire of the quantum circuitextends through multiple slices of quantum circuit.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S)

Having thus described the invention in general terms, reference will nowbe made to the accompanying drawings, which are not necessarily drawn toscale, and wherein:

FIG. 1 provides a schematic diagram of an example system, in accordancewith an example embodiment.

FIG. 2 provides a schematic diagram of an example domain divided intosections, in accordance with an example embodiment.

FIGS. 3A&B provide schematic diagrams of an example quantum circuit andthe slicing of the example quantum circuit, in accordance with anexample embodiment.

FIG. 4 provides a flowchart illustrating various processes, procedures,and/or operations performed by a quantum computer for executing aquantum circuit with efficient qubit usage.

FIG. 5 provides a schematic diagram of an example user computing entitythat may be used in accordance with an example embodiment.

FIG. 6 provides a schematic diagram of an example quantum computer thatmay be used in accordance with an example embodiment.

DETAILED DESCRIPTION OF SOME EXAMPLE EMBODIMENTS

The present invention now will be described more fully hereinafter withreference to the accompanying drawings, in which some, but not allembodiments of the invention are shown. Indeed, the invention may beembodied in many different forms and should not be construed as limitedto the embodiments set forth herein; rather, these embodiments areprovided so that this disclosure will satisfy applicable legalrequirements. The term “or” (also denoted “/”) is used herein in boththe alternative and conjunctive sense, unless otherwise indicated. Theterms “illustrative” and “exemplary” are used to be examples with noindication of quality level. The terms “generally” and “approximately”refer to within engineering and/or manufacturing limits and/or withinuser measurement capabilities, unless otherwise indicated. Like numbersrefer to like elements throughout.

I. Overview

Computing the dynamical properties of electronic and magnetic materialsis useful for predicting many of their technologically importantphysical properties such as optical absorption and emission spectra,alternating current (AC) conductivity, magnetic susceptibility,magnetoresistance, spin-dynamics, and many other properties. Classicalsimulation of the dynamics of correlated quantum systems is extremelychallenging, due to rapid growth of entanglement entropy, which limitsstate-of-the-art simulation methods like time-dependent density-matrixrenormalization group (DMRG) to very short time-scales.

Quite generally, the memory and simulation time resources to classicallysimulate the dynamics of quantum systems grow exponentially in thesystem-size or final simulation time. In contrast, the advent ofprogrammable quantum computers enables a variety of polynomial timealgorithms for simulating quantum materials, which offer an exponentialreduction in the resources required for conducting these simulations.However, near-term quantum computing hardware will have access to only alimited number (10's to 100's) of quantum bits (qubits), and will alsobe strongly limited by noise and gate errors.

Various embodiments of the present invention provide methods,apparatuses, computing entities, computer program products, systems,and/or the like for executing quantum circuits with efficient qubitusage such that a relatively small number of potentially noisy qubitsmay be used to solve complex problems that may be very difficult and/orintractable to solve via classical computing means.

In various embodiments, a quantum computer implements a circuit of largewidth on a large number of “system qubits” (e.g., qubits evolved alongsystem qubit wires of the circuit) using only a limited number of“physical qubits”. First, the past causal cone of the quantum circuitoutput for the left-most system qubit wires is identified, whichcontains a subset of the system qubit wires along with at least oneancilla qubit. For example, the past causal cone of a first system qubitwire at the fully evolved level is identified and used to define thefirst slice 140A, as shown in FIG. 3A. For a given qubit in the circuit,we can define its past causal cone as the set of all qubits from whichthe given qubit can be reached by tracing the wires from past to future,exiting each gate by any of the wires flowing out of it. From thisdefinition, the past causal cone of the qubits at the top of systemqubit wires 1 and 2 shown in FIG. 3A contains all qubits to thelower-left of the dashed line (e.g., boundary 146) (including the qubitsentering along system qubit wires 1-5, along with all qubits enteringalong the ancilla wires).

The quantum computer has sufficient physical qubits to process therestriction of the complete circuit contained within this past causalcone (the five left-most system qubit wires 120 on the bottom of thecircuit in FIGS. 3A and 3B and the ancilla wires 110). The qubitsevolved along these system qubit wires to the fully evolved level of thequantum circuit (e.g., at the output of this cone, labeled A and B inFIG. 3B) are measured if desired, reinitialized, and recycled back tothe base level of the circuit, where they may be used to expand thecausal cone by a slice to the right of the initial cone, encompassingmore system qubits at the circuit output [in this case the 3rd and 4thqubits from the left at the top of the circuit, labeled C and D]. Thisprocess may be repeated to process and/or perform more slices of thecircuit, until all of the slices of the quantum circuit have beenprocessed and/or performed. At this point the entire quantum circuit hasbeen faithfully executed and all desired measurements on the fullyevolved level of the circuit have been obtained.

In various embodiments, a quantum circuit is defined. In variousembodiments, the quantum circuit comprises a plurality of system qubitwires. In an example embodiment, a physical system or domain beingmodeled and/or simulated is discretized onto a lattice using anysuitable technique (e.g., a tight-binding description of the material).Each point in that lattice contains a finite number (e.g., at mostd_(s)) of quantum degrees of freedom. For example, the domain beingmodeled and/or simulated may be a 1-dimensional, 2-dimensional, or3-dimensional physical system and/or domain (e.g., at least a portion ofa physical material) and each system qubit wire may represent, model,simulate, and/or correspond to the evolution (e.g., in time) of aquantum degree of freedom, physical location, and/or particle within thesystem and/or domain. For example, a system qubit wire of the quantumcircuit may simulate the evolution (e.g., in time) of one or moreproperties of a corresponding section within the system and/or domain.For example, the quantum circuit may simulate the dynamics of theevolution of quantum states of particles within a physical domain. Invarious embodiments, the domain may not be a physical domain and thedomain may be more than 3-dimensional. For example, the domain maycorrespond to the spread of disease through a geographical area,logistics operations in a geographical area, financial indices, and/orother one or multi-dimensional domains.

In various embodiments, time evolution and/or interaction betweensections of a domain (and/or locations and/or particles and/orcorresponding degrees of freedom within a section) are simulated and/ormodeled via an operator. For example, a domain may be divided intosections. If the dimensionality of the domain is d, the dimensionalityof each section is d−1. In various embodiments, the operator is aHamiltonian. In various embodiments, the operator is a local operator.An operator H(t) is a local operator when H(t)=Σ_(k) h_(k)(t), where kindexes successive (e.g., spatially adjacent) d−1 dimensional sectionsof the d dimensional lattice, and each operator term h_(k)(t) acts onlattice sites that are contained within a section of distance of at mostpositive integer p from section k. For example, if the system and/ordomain is a one dimensional system and/or domain, a section is zerodimensional (e.g., corresponds to a particular point within the systemand/or domain) and each operator term h_(k)(t) acts on at most pneighboring points of the system and/or domain. For example, FIG. 2illustrates an example one dimensional system and/or domain 200 that hasbeen divided into a plurality of sections 202 (e.g., 202.1, 202.2,202.3, 202.4, 202.k). In an example embodiment, where p=2, h₁(t) may acton degrees of freedom relating to sections 202.1, 202.2, and 202.3 butwill not act on degrees of freedom in section 202.4. In another exampleembodiment, if the domain is a three dimensional domain, a section istwo dimensional (e.g., a plane) and each operator term h_(k)(t) actswithin the two dimensional section and on degrees of freedom/points atmost p sections from section k. For example, the operator term h_(k)(t)does not act on every degree of freedom, location, and/or particlewithin the domain. For example, the operator term h_(k)(t) may encodegeometrically local interactions.

In various embodiments, the quantum circuit comprises one or moreancilla wire. In various embodiments, each ancilla qubit (e.g., a qubitbeing evolved along an ancilla wire) prepares correlations betweenvarious qubit wires (and/or the degrees of freedom of the domainrepresented thereby) that are present in the initial state correspondingto one or more initial properties of the domain across a section of thedomain. For example, when a system qubit (e.g., a physical qubit beingevolved along a system qubit wire 120) interacts with an ancilla qubit(e.g., a physical qubit being evolved along an ancilla wire 110) via aunitary gate 112 (see FIGS. 3A and 3B), the ancilla qubit impartscorrelations between the initial state of various degrees of freedom invarious sections. In an example embodiment, the ancilla qubits (e.g.,qubits being evolved along ancilla wires) generate a matrix productstate between the degrees of freedom in the various sections of thedomain at the initial time t=0. In various embodiments, each systemqubit is first initialized onto a system qubit wire, and then broughtinto a correlated state through interaction with one or more ancillaqubits via unitary gates. The system qubit then continues to be evolvedalong the system qubit wire by being gated with other system qubits(e.g., qubits being evolved along other system qubit wires) in order tosimulate time evolution of the simulated system and/or domain under alocal Hamiltonian.

In various embodiments, slices of the quantum circuit are defined. Asdescribed above, the quantum circuit comprises a plurality of systemqubit wires that extend from the base level of the quantum circuitcorresponding to time t=0 to the fully evolved level corresponding totime t=T. The quantum wires each relate to one or more degrees offreedom of a section of the simulated system and/or domain. A systemqubit wire may pass through one or more slices of the quantum circuit.

In various embodiments, the quantum circuit is executed slice by slice140 starting with the first slice 140A on the left side of FIG. 3B andmoving left to right through each successive slice 140. For example,first, all gates within the first slice 140A (the triangular region) areexecuted, and any desired measurements of the qubits at the output ofthat slice 140A (e.g., fully evolved level 136) are made. Then, thephysical qubits that have made it to the fully evolved level 136 (e.g.,the top of the slice labeled A and B in FIG. 3B) are reset (e.g.,reinitialized) and inserted at the bottom of the system qubit wires(e.g., base level 130) in the next slice 140. The gates within thatslice 140 are then executed in accordance with the time ordering of thecircuit (for example, red gates first, and then blue gates in ascendingorder from bottom to top). In the example FIG. 3B, the gates executed atthis point in the procedure are light-shaded. The physical qubits thathave made it to the top of this second slice 140B (labeled C and D inFIG. 3B) are then reset (e.g., reinitialized) and inserted back into thebottom of the third slice 140. At this point the gates in that thirdslice can be executed, and the procedure continues from left to rightthrough all slices 140 until all gates 112, 122 have been executed, andall measurements 150 have been made.

In various embodiments, each slice of the quantum circuit begins at abase level of the quantum circuit and extends diagonally across thesystem qubit wires of the quantum circuit up to a fully evolved level.For example, if the quantum circuit simulates and/or models theevolution of the system and/or domain from time t=0 to time t=T, thebase level of the quantum circuit corresponds to time t=0 and the fullyevolved level corresponds to time t=T. In various embodiments, the i=1slice is defined such that at least one system qubit wire is evolvedfrom the base level to the fully evolved level, and must exclusivelycontain the complete past causal cone of the at least one system qubitwire at the fully evolved level. The past causal cone is defined byidentifying all system qubits at the base level that can be connected tothe fully evolved qubits by following wires through the gates in thedirection of the arrows shown in FIGS. 3A and 3B. For example, a systemqubit wire that reaches the fully evolved level in the i=1 slice isevolved from the base level to the fully evolved level withoutinteraction with and/or evolution of any of the system qubit wiresstarting in the base level of the i>1 slices. In various embodiments,the i>1 slices may be defined recursively. For example, for a i≥1, the+1 slice can be identified by taking the system qubit wires immediatelyto the right of the system qubit wires at the fully evolved level of theith slice of the quantum circuit and then identifying the past causalcone of those system qubit wires immediately to the right of the systemqubit wires at the fully evolved level of the ith slice. The systemqubit wires immediately to the right of the system qubit wires at thefully evolved level of the ith slice include the system qubit wires thatare directly connected by gates at the fully evolved level. The part ofthe identified past causal cone that does not intersection with slicei−j, for any non-negative integer j, is slice i+1. For example, a systemqubit wire that reaches the fully evolved level in an i>1 slice isevolved to the fully evolved level without interaction with and/orevolution of any of the system qubit wires starting at and/or extendingfrom the base level of an i+j slice, where j is a positive integer.Execution of an i>1 slice may include interaction with and/or evolutionof one or more system qubit wires that started at and/or extend from thebase level of an i−j slice, where j is a positive integer. In general,for a system qubit wire that reaches the fully evolved level in slice imay be gated with system qubit wires that originate (e.g., at the baselevel of the quantum circuit) from any of slices i−j,j any non-negativeinteger and not gated with system qubit wires that originate (e.g., atthe base level of the quantum circuit) from any of slices i+j.

In various embodiments, the quantum circuit is executed slice by slice.For example, the quantum computer may execute a first slice of thequantum circuit such that one or more system qubit wires are initializedat the base level of the first slice and at least one system qubit wireis evolved to the fully evolved level of the first slice. A second sliceof the quantum circuit may then be executed such that one or more systemqubit wires are initialized at the base level of the second slice and atleast one system qubit wire is evolved to the fully evolved level of thesecond slice. A third slice of the quantum circuit may then be executedand so on, until each slice of the quantum circuit has been executed.

In various embodiments, measurements may be taken of one or moreproperties of a qubit at various points of the evolution of the qubitalong the corresponding qubit trace to determine one or more propertiesof the corresponding location and/or particle of the domain at thecorresponding time. For example, when a physical qubit being evolvedalong a system qubit wire reaches the fully evolved level of the quantumcircuit, one or more measurements may be taken to determine one or moreproperties of the location and/or particle corresponding to the systemqubit wire at the time t=T. In various embodiments, once a physicalqubit is evolved along a system qubit wire to the fully evolved level ofslice i, and any desired measurements are made, it may be initializedand reintroduced at the base level of slice i+1 to be evolved alonganother system qubit wire.

In various embodiments, the execution of the quantum circuit in a sliceby slice manner allows the for recycling of physical qubits. Forexample, by executing the quantum circuit in a slice by slice manner, aphysical qubit of the quantum computer may be initialized along aplurality of system qubit wires of different slices. Thus, fewerphysical qubits are required to fully execute the quantum circuit.Thereby, embodiments enable the execution of quantum circuits modelingand/or simulating complex system using a relatively small number ofqubits.

II. Example System Architecture

FIG. 1 provides a schematic diagram of an example system that may beused in accordance with an example embodiment. In various embodiments,the system comprises a user computing entity 10 and a quantum computer30. In various embodiments, the quantum computer 30 comprises acontroller 500, a plurality of qubits, and one or more qubit managementsystems. In various embodiments, the user computing entity 10 maycommunicate via wired or wireless communication with the controller 500of the quantum computer 30. In various embodiments, the user computingentity 10 may be in direct communication with the controller 500 or maycommunicate with the controller 500 via one or more networks 20.

In various embodiments, a user computing entity 10 is configured toallow a user to provide input to the quantum computer 30 (e.g., via auser interface of the user computing entity 10) and receive, view,and/or the like output from the quantum computer 30. The user computingentity 10 may be in communication with the quantum computer 30 (e.g.,controller 500) via one or more wired or wireless networks 20. Invarious embodiments, the quantum computer 30 may be a trapped ionquantum computer, nuclear magnetic resonance quantum computer,superconducting quantum computer, photonic quantum computer, and/orother kind of quantum computer.

In various embodiments, the controller 500 is configured to control oneor more qubit management systems of the quantum computer 30 so as tomanipulate and/or evolve one or more qubits of the quantum computer 30in a desired manner. For example, the controller 500 may be configuredto execute one or more quantum circuits by causing the one or more qubitmanagement systems to manipulate and/or evolve the one or more qubits ina manner indicated and/or defined by the quantum circuit. For example,the one or more qubit management systems may comprise thermal controlsystems (e.g., cryogenic cooling systems), vacuum systems (e.g.,pressure control systems), qubit confinement systems (e.g., an ion trapand voltage sources connected to the ion trap in the case of a trappedion quantum computer), one or more gate systems (e.g., lasers andcorresponding optics in the case of a trapped ion quantum computer),measurement systems (e.g., including optics, photodetectors, and/or thelike in the case of a trapped ion quantum computer), and/or the like. Bycausing the one or more qubit management systems to manipulate and/orevolve the one or more qubits in accordance with the quantum circuit,the quantum computer 30 may perform calculations, simulations, generatemodels, and/or the like.

The user computing entity 10 may provide (e.g., transmit) quantumcircuit(s), executable code portions (e.g., computer executableinstructions, command sets, and/or the like) encoding the quantumcircuit(s), and/or requests for the execution of one or more quantumcircuits such that the controller 500 of the quantum computer 30receives the quantum circuit(s), the executable code portions encodingthe quantum circuit(s), and/or the requests. The quantum computer 30 maythen execute a quantum circuit and determine, measure, and/or the likeresults of the execution of the quantum circuit, possibly in response toreceiving a quantum circuit, executable code portions encoding thequantum circuit, and/or the request for the execution of a quantumcircuit. The quantum computer 30 may then provide (e.g., transmit) theresults of the execution of the quantum circuit and/or a result ofprocessing the results of the execution of the quantum circuit such thatuser computing entity 10 receives the results of the execution of thequantum circuit and/or a result of processing the results of theexecution of the quantum circuit. The user computing entity 30 may thenuse the results of the execution of the quantum circuit and/or a resultof processing the results of the execution of the quantum circuit asinput to one or more programs, cause the results of the execution of thequantum circuit and/or a result of processing the results of theexecution of the quantum circuit to be displayed via a user interface ofthe user computing entity 10, cause the results of the execution of thequantum circuit and/or a result of processing the results of theexecution of the quantum circuit to be stored in computer-readablememory, and/or the like.

III. Example Quantum Circuit

In various embodiments, a quantum circuit is a model for a quantumcomputation in which the quantum computation is a sequence of quantumgates. In various embodiments, the quantum circuit is divided into aplurality of slices. Executing the quantum circuit includes executingthe slices in series. FIGS. 3A and 3B provide diagrams of an examplequantum circuit 100. The quantum circuit 100 comprises a plurality ofsystem qubit wires 120 (e.g., 120A, 120B). The quantum circuit 100comprises a plurality of levels, starting with a base level 130 at whicheach system qubit wire begins with an initialization step and extendingthrough a plurality of levels to a fully evolved level 136. As usedherein a system qubit is a physical qubit 555 of the quantum computer 30that is being evolved along a system qubit wire 120. Note that a singlephysical qubit 555 may, at various points in the algorithm, play therole of multiple different system qubits as a result of the qubit reusescheme described herein. For example, a single physical qubit 555 may besuccessively re-introduced onto multiple system qubit wires afterreaching the fully evolved state of a previous system qubit wire.

In various embodiments, the plurality of levels between the base level130 and the fully evolved level 136 may comprise a unitary circuit level132. In various embodiments, the quantum circuit 100 comprises one ormore ancilla wires 110. As used herein an ancilla qubit is a physicalqubit 555 of the quantum computer 30 that is being evolved along anancilla wire 110. In various embodiments, the unitary circuit level 132includes the interaction of an ancilla wire 110 with a system qubit wire120. For example, an ancilla qubit may interact with the system qubitbeing evolved along the system qubit wire 120, for example, via a gate112 (e.g., 112A, 112B). The interaction of the ancilla qubit and thesystem qubit via the gate 112 may cause the system qubit to be in astate corresponding to and/or approximating an initial state for thelocation and/or particle corresponding to the corresponding system qubitwire 120. For example, the interaction of the ancilla qubits and thesystem qubits may cause the system qubits to be in a state thatapproximates the lowest energy state of a Hamiltonian. The intermediatelevels 134 (e.g., 134A, 134B) may correspond to the time evolutionand/or interaction(s) between neighboring locations and/or particleswithin the domain, as described by an operator (e.g., Hamiltonian). Forexample, the intermediate levels 134 of a system qubit wire 120 maycomprise interaction gates 122 (e.g., 122A, 122B) causing the timeevolution and/or interaction between physical qubits being evolved alongother system qubit wires. In contrast to physical qubits 555 evolvedalong system qubit wires 120, a physical qubit 555 evolved along anancilla wire 110 will not be reused, in various embodiments.

In various embodiments, the quantum circuit 100 may include the takingof one or more measurements 150 (e.g., 150A, 150 n. For example, themeasurements 150 may indicate one or more properties of a locationand/or particle within the domain at a corresponding time. For example,if measurements 150A are made of a first physical qubit evolved along afirst system qubit wire 120A at fully evolved level 136, themeasurements 150A indicate one or more properties corresponding to afirst location or particle at the time t=T. The quantum circuit 100 maycomprise a variety of measurements at different levels 134, 136 withinthe circuit and/or along different system qubit wires 120 as appropriatefor the computation modeled by the quantum circuit 100.

The quantum circuit 100 has an implied time ordering whereby all systemqubit (i.e. vertical) wires 120 run from the bottom (past) to the top(future), and the ancilla (i.e. horizontal) wires 110 run from the left(past) to the right (future). This direction is indicated by arrows on asubset of the wires in FIGS. 3A and 3B, though it exists in a similarmanner for all of the wires.

In various embodiments, the quantum circuit 100 is divided into and/orcomprises a plurality of slices 140 (e.g., 140A, 140B, . . . , 140 n). Aslice 140 of the quantum circuit 100 extends from the base level 130 tothe fully executed level 136 in a diagonal manner compared to the systemqubit wires 120. For example, slice boundaries 146 (shown as the dottedlines in FIG. 3 ) may cross one or more system qubit wires 120. Forexample, an i-th slice 140 i of the quantum circuit 100 may correspondto a base level qubit set 142 i (e.g., 142A, 142B) and a fully evolvedlevel qubit set 144 i (e.g., 144A, 144B). The base level qubit set 142 icomprises at least one system qubit wire 120 and the fully evolved levelqubit set 144 i comprises at least one system qubit wire 120. However,the base level qubit set 142 i and the fully evolved level qubit set 144i may not have any overlap. For example, the fully evolved level qubitset 144 i of the i-th slice 140 i may not include any of the systemqubit wires 120 in the base level qubit set 142 i of the i-th slice 140i. In other words, a system qubit wire 120 may begin, at the base level130, in the base level set 142 i of the i-th slice and may reach thefully evolved qubit set 144(i+j) of the i+j-th slice 140(i+j), where jis a positive integer. For example, the i-th slice 140 i extendsdiagonally across the intermediate levels 134 (e.g., 134A, 134B) to thefully evolved level 136.

In an example embodiment, for i>1, the base level qubit set 142 i andthe fully evolved level qubit set 144 i include the same number ofsystem qubit wires 120. In an example embodiment, for i, j>1, the baselevel qubit set 142 i of the i-th slice and the base level qubit set 142j of the j-th slice include the same number of system qubit wires 120.In an example embodiment, the fully evolved level qubit set 144A of thefirst slice 140A includes the same number of system qubit wires 120 asthe fully evolved level qubit set 144 i of the i-th slice 140 i. Invarious embodiments, the base level qubit set 142A of the first slice140A includes a larger number of system qubit wires 120 compared to thebase level qubit set 144 i of the i-th slice 140 i. In an exampleembodiment, the base level qubit set 142A of the first slice 140Aincludes the minimum number of system qubit wires 120 required for atleast one system qubit wire 120 of the base level qubit set 142A to befully evolved. For example, the first slice 140A may be the only slice140 for which there exists an overlap between the base level qubit set142A and the fully evolved level qubit set 144A.

In various embodiments, the quantum circuit 100 is a circuit and/oralgorithm to simulate the dynamics |ψ(t)>=U(t)|ψ(0)>=τ[e^(−i∫) ⁰ ^(t)^(H(s)ds)]|ψ(0)> of the evolution of quantum states |ψ(0)>, representedas a matrix product state (MPS) with bond-dimension χ, subjected to ageometrically local (possibly time-dependent) operator that takes theform of a Hamiltonian, H(t). Here τ—denotes the time-ordered product.MPS's can represent any pure- or mixed-quantum states for sufficientlylarge bond-dimension χ. Classical computing methods for MPS'sgenerically require computing time and memory resources that scalepolynomially in the bond-dimension χ, typically limiting them toshort-time dynamics and to one-dimensional or quasi-one-dimensionalsystems. In contrast, various embodiments enable an exponentialreduction in the bond-dimension χ-dependence of quantum computationalresources, enabling computations to be performed for a much larger rangeof quantum states, longer-time ranges, and higher-dimensional (e.g.,2-dimensional and 3-dimensional) materials and/or domains.

In various embodiments, the domain to be simulated and/or modeled isapproximated by a discrete mesh with a finite number, d_(s), of quantumdegrees of freedom per site, using any standard orbital basis (e.g. atight-binding description) for the electronically relevant orbitals.Various embodiments are agnostic to the particular choice of orbitalbasis. Various embodiments simulate and/or model time-dynamics generatedby a local Hamiltonian H(t)=Σ_(k) h_(k)(t), where, as used herein theterm “local” means that each term, h_(k)(t), acts on lattice sites thatare contained within sections of distance of at most positive integer pfrom section k.

To simulate dynamical properties over a range of times time intervalst∈[0, T], of a system or domain discretized onto a lattice of integerlinear and cross-sectional dimensions L×A, with accuracy ˜ε, variousembodiments require

$\left. N_{Q} \right.\sim{O\left( {{\frac{T^{2}}{\epsilon}pA\log_{2}d_{s}} + {\log_{2}\chi}} \right)}$

physical qubits and a quantum circuit depth

${\left. D \right.\sim{O\left( {L\frac{T^{2}}{\epsilon}} \right)}}.$

Here L is the number of lattice points/sites in the direction alongwhich the lattice is being divided into sections and A is the number oflattices points/sites contained within each section. In an exampleembodiment, the system and/or domain is divided into sections along itslongest dimension, which makes the algorithm more efficient. Forexample, the sections may be taken orthogonal and/or transverse to thelongest dimension of system and/or domain.

In various embodiments, quantum circuits 100 divide the physical quoitsinto

$N_{s} = {O\left( {\frac{T^{2}}{\epsilon}p\ A\ \log_{2}d_{s}} \right)}$

qubits moving along the system qubit wires, prepared in some fixedinitial state, which iteratively interact with a register ofN_(a)˜O(log₂ χ) additional ancilla wire. Strategic use of opportunisticmeasurement and reset and re-use of physical qubits serially along oneor more system qubit wires enable various embodiments to simulate verylarge systems with a relatively small number of qubits.

In various embodiments, the quantum circuit may be defined, generated,and/or determined as follows. In various embodiments, the continuoustime-evolution by the Hamiltonian of the quantum state of the locationsand/or particles of the domain is decomposed into a discrete quantumcircuit of N levels (e.g., 130, 132, 134, 136) of disjoint terms actingon p sections of the simulated system and/or domain. In variousembodiments, this decomposition of the time-evolution is performed usinga variety of standard methods. For example, in an example embodiment,the Trotter-Suzuki formula

${{U(t)} = {{\mathcal{T}\left\lbrack e^{{- i}{\int_{0}^{t}{{H(s)}{ds}}}} \right\rbrack} \approx {{\prod_{\alpha = 1}^{N}{\prod_{\mu = 1}^{p}\left( {\prod_{{i = \mu},{\mu + p},\ldots}e^{{- \frac{iT}{N}}{h_{i}(t_{\alpha})}}} \right)}} + {O\left( \frac{T^{2}}{N} \right)}}}},{{{with}t_{\alpha}} = {\alpha\frac{T}{N}}}$

(this equation represents only the simplest Trotter decomposition, butcan be straightforwardly generalized to higher-order version of theTrotter-Suzuki decomposition) is used to perform the decomposition. Theinitial matrix product state may be defined and/or determined andtensors V_(α,β) ^(σ) in left-canonical form may be extracted therefrom.In various embodiments, the interactions between ancilla qubits (e.g.,qubits being evolved along ancilla wires 110) and system qubits (e.g.,qubits being evolved along system qubit wires 120) may be defined basedon the tensors V_(α,β) ^(σ) extracted from and/or determined by theinitial matrix product state for the domain. Without loss of generality,it is assumed that the tensors are in left-canonical form, such thatV_(α,β) ^(σ) is an isometry, and can be implemented by a unitary circuitU_(V) acting on the ancilla and system qubits, with the system qubitsinitialized in a fixed initial state |0> (at the base level 130). In anexample embodiment, the unitary circuit U_(V), the tensors V_(α,β) ^(σ),and the fixed initial state |0> satisfy <σ, α|U_(V)|0, β>=V_(α,β) ^(σ).In various embodiments, the unitary circuit U_(V) is generated either byprior knowledge of the state, or by variationally optimizing aparameterized family of circuits, for example, to variationallyapproximate the lowest energy state of the Hamiltonian of the materialand/or domain being modeled and/or simulated. In various embodiments,the result is a quantum circuit 100 that may then be divided into aplurality of slices 140.

In various embodiments the time-evolution quantum circuit 100 isimplemented on a quantum computer with N_(a)=O(log₂ χ) ancilla qubits,which interact with system qubits along (LA log₂ d_(s)) system qubitwires 120 represented by only

$N_{s} = {O\left( {\frac{T^{2}}{\epsilon}p\ A\ \log_{2}d_{s}} \right)}$

physical qubits. The quantum circuit is divided into a plurality ofslices 140 each having a fully evolved level qubit set 144 including O(pA log₂ d_(s)) system qubit wires and a sequence of quantum gates toimplement the U_(V) and the operations

$e^{{- \frac{iT}{N}}h_{i}}.$

For example, the example quantum circuit 100 shown in FIG. 3 correspondsto A=1, d_(s)=2, and p=2.

The quantum circuit 100 may then be executed. In various embodiments,each level of the first slice 140A is executed across each level inorder from the base level 130, then the unitary circuit level 132, thenthe intermediate levels 134 in order (e.g., the first intermediate level134A, then the second intermediate level 134B, and so forth), until thefully evolved level 136 is reached. For example, each physical qubitthat will be evolved along a system qubit wire 120 of the base levelqubit set 142A of the first slice 140A is initialized into the fixedinitial state |0>. Then the physical qubits that will be evolved alongthe ancilla wires 110 are initialized and the circuit implementing theunitary circuit U_(V) is applied to the physical qubits being evolvedalong the ancilla wires 110 and physical qubits being evolved along thesystem qubit wires 120 of the first slice 140A at gates 112 (e.g., 112A,112B). The interaction gates 122 (e.g., 122A, 122B) are executed of eachintermediate level 134 until the fully executed level 136 is reached. Invarious embodiments, the interaction gates 122 implement

$e^{{- \frac{iT}{N}}h_{k}}$

to the physical qubits being evolved along the system qubit wires 120 ofthe first slice 140A. Once the first slice 140A has been fully executed,the physical qubits evolved along the system qubit wires 120 of thefully evolved level qubit set 144A of the first slice are reset andinitialized onto the system qubit wires 120 of the base level qubit set142B of the second slice 140B.

For i>1, the i-th slice may be executed by resetting the physical qubitsthat were evolved along the system qubit wires 120 of the i−1-th slicefully evolved level qubit set 144(i−1) such that those physical qubitsare initialized into the fixed initial state |0> at the base level 130of the i-th slice 140 i (e.g., on the system qubit wires 120 of the baselevel qubit set 142 i of the i-th slice 140 i). The unitary circuitgates 112 of the i-th slice 140 i are executed at the unitary circuitlevel 132 of the i-th slice. The interaction gates 122 of the firstintermediate level 134A are then executed to implement

$e^{{- \frac{iT}{N}}h_{k}}.$

The remaining intermediate levels 134 are then executed in order as theslice 140 i crosses system qubit wires 120 that were initialized inprevious slices 140(i−j) until the fully evolved level 136 is reached.The process may then be repeated for the i+1-th slice 140(i+1), untilall of the slices have been fully executed.

This procedure gives access to any measurable quantities of thetime-evolved state, by measuring a desired observable on the physicalqubits evolved along a system qubit wire 120 at the fully evolved level136, before resetting the physical qubits for re-use in the next slice.To measure observables at intermediate times, one can simply interruptthe execution of the quantum circuit 100, and perform measurement of thedesired observable on the physical qubit at the desired time (e.g., atthe intermediate level 134 corresponding to the desired time).

IV. Example System Operation

FIG. 4 provides a flowchart illustrating various processes, procedures,and/or operations performed by a quantum computer 30 for executing aquantum circuit with efficient qubit usage. Starting at step/operation302, a quantum circuit 100 is defined and slices 140 of the quantumcircuit are determined and/or defined. In an example embodiment, thequantum circuit 100 and/or the slices 140 of the quantum circuit may bedefined by a user computing entity 10 (e.g., either automatically (e.g.,by a machine user) or via user interaction with a user interface) and/orby a controller 500 of the quantum computer 30. In an exampleembodiment, the quantum circuit 100 may be defined by the user computingentity 10 and provided such that the controller 500 of the quantumcomputer 30 receives the quantum circuit 100 and defines the slices 140of the quantum circuit. In an example embodiment, the quantum circuit100 and the slices 140 of the quantum circuit are defined by the usercomputing entity 10 and provided such that the controller 500 of thequantum computer 30 receives the quantum circuit 100 with the slices 140thereof already defined. For example, the user computer entity mayprovide the quantum circuit 100 with the slices 140 of the quantumcircuit defined. The controller 500 may then receive (e.g., at theprocessing device 505 via the communication interface 520) the quantumcircuit 100 with slices 140 thereof defined. In various embodiments, nslices 140 of the quantum circuit 100 are defined.

At step/operation 304, the physical qubits that are to be evolved alongthe system qubit wires of the first slice 140A are initialized (e.g.,the physical qubits to be evolved along the system qubit wires 120 ofthe base level qubit set 142A of the first slice 140A). For example, thebase level 130 of the first slice 140A may be executed. For example, thecontroller 500 (e.g., via the processing device 505, the drivercomponent elements 515, and/or the like) may cause one or more qubitmanagement systems 550 to manipulate physical qubits 555 of the quantumcomputer 30 such that physical qubits are initialized onto the systemqubit wires 120 of the base level qubit set 142A of the first slice 140Aand onto the ancilla wires 110. For example, the index i is initializedat 1 and the base level 130 of the i-th slice is executed.

At step/operation 306, the unitary circuit level 132 of the i-th sliceis executed. For example, the controller 500 (e.g., via the processingdevice 505, the driver component elements 515, and/or the like) maycause one or more qubit management systems 550 to manipulate physicalqubits 555 of the quantum computer 30 such that the unitary circuitlevel 132 of the i-th slice is executed. For example, the unitary U_(V)may be applied to the physical qubits being evolved along the ancillawires 110 and the system qubit wires 120 across the unitary circuitlevel 132 of the i-th slice. For example, unitary circuit gates 112 maybe applied to the physical qubits being evolved along the ancilla wires110 and physical qubits being evolved along system qubit wires 120 ofthe i-th slices.

At step/operation 308, the circuits applying the time evolution of thesystem qubit wires 120 of the i-th slice are executed. For example, theintermediate levels 134 of the i-th slice are executed in order. Forexample, the first intermediate level 134A may be executed, followed bythe second intermediate level 134B, and so on until the fully evolvedlevel 136 of the i-th slice is achieved. In various embodiments, thecontroller 500 (e.g., via the processing device 505, the drivercomponent elements 515, and/or the like) may cause one or more qubitmanagement systems 550 to manipulate physical qubits 555 of the quantumcomputer 30 such that the interaction gates 122 are executed inaccordance with the intermediate levels 134 of the quantum circuit 100.

At step/operation 310, any desired measurements corresponding to fullyevolved qubit set 144 i of the i-th slice are captured. For example, thecontroller 500 (e.g., via the processing device 505, the drivercomponent elements 515, and/or the like) may cause one or more qubitmanagement systems 550 to manipulate physical qubits 555 of the quantumcomputer 30 such that any desired measurements of the physical qubits555 that were evolved (e.g., along system qubit wires 120) to the fullyexecuted level 136 of the i-th slice are captured. Step/operation 310may be, but is not required to be, initiated after the completion ofstep 308, and may, for example, be implemented simultaneously withstep/operation 308, such that measurements can be made at intermediatecircuit levels 134.

At step/operation 312, the controller 500 (e.g., via the processingdevice 505 and/or the like) may determine whether the index i is equalto n, the number of slices of the circuit. When it is determined, atstep/operation 312, that the index i is not equal to n, the processcontinues to step/operation 314.

At step/operation 314, the physical qubits evolved along the systemqubit wires 120 of the fully executed level qubit set 144 i of the i-thslice are reset so that they may be initialized in the base level 130 of(i+1)-th slice 140(i+1). For example, the controller 500 (e.g., via theprocessing device 505, the driver component elements 515, and/or thelike) may cause one or more qubit management systems 550 to manipulatephysical qubits 555 of the quantum computer 30 such that the physicalqubits evolved along the system qubit wires 120 of the fully executedlevel qubit set 144 i of the i-th slice are reset such that they may beinitialized onto the system qubit wires of the base level qubit set142(i1) of the (i+1)-th slice. For example, once a physical qubit hasbeen fully evolved along a system qubit wire 120 (e.g., reached thefully evolved level 136), the physical qubit 555 may be re-initializedonto another system qubit wire starting in a subsequent slice of thequantum circuit. In this manner, physical qubits may be reused withinthe execution of the quantum circuit 100 to reduce the total number ofphysical qubits 555 needed to execute the quantum circuit.

At step/operation 316, the controller 500 increments the index i. Forexample, the controller (e.g., via the processing device 505 and/or thelike) may increment the index i to the value i+1. For example, the indexi may be incremented and the next slice may be executed.

When, at step/operation 312, it is determined by the controller 500 thatthe index i=n (the number of slices of the quantum circuit 100), theprocess continues to step/operation 318. At step/operation 318, theexecution of the quantum circuit 100 is determined to be complete andthe controller 500 may provide the results of the execution of thequantum circuit 100. For example, the controller 500 (e.g., by theprocessing device 505 via the communication interface 520, and/or thelike) may provide the measurements captured during the execution of thequantum circuit 100. For example, the controller 500 may provide theresults of executing the quantum circuit 100 such that the usercomputing entity 10 receives the results of executing the quantumcircuit 100. The user computing entity 10 may then use the results asinput to one or more processes (e.g., to analyze the results ofexecuting the quantum circuit and/or the like), cause at least a portionof the results of executing the quantum circuit 100 to be displayedand/or provided via a user interface of the user computing entity 10(e.g., via display 416), cause at least a portion of the results ofexecuting the quantum circuit 100 to be stored in memory (e.g., memory422, 424), and/or the like.

V. Technical Advantages

Various embodiments provide technical solutions to the technical problemof simulating the dynamics of a domain under the influence of a localoperator (e.g., a local Hamilton) using a quantum computer that has arelatively small number of potentially noisy qubits. For example,various embodiments allow the use of a quantity of qubits (e.g., 1-500qubits, 10-100 qubits, 20-50 qubits, and/or the like) to simulate thedynamics of a physical domain (e.g., a much larger physical domain)under the influence of a local operator (e.g., a local Hamiltonian) thatwould be very computationally expensive and/or intractable usingclassical computing means. In various embodiments, the dividing of aquantum circuit into slices and the executing of the slices in orderallows for the re-use of physical qubits along various qubit traces,thereby reducing the number of physical qubits needed to perform thecomputation (e.g., execute the quantum circuit). Various embodimentseffectively reduce the dimensionality of the system and/or domain beingsimulated by one. For example, a one dimensional system of length L_(x)may be simulated, in an example embodiment, using only a small number(independent of length L_(x)) of physical qubits. In another example, atwo dimensional system and/or domain of dimensions L_(x), L_(y) may besimulated, in an example embodiment, using a number of qubits thatscales with L_(y) (which may be selected to be the smaller/shorter ofthe two lengths L_(x), L_(y)) but is independent of L_(x). Embodimentstherefore provide an improvement to the functioning of a quantumcomputer by enabling complex computations to be performed using fewerqubits.

VI. Exemplary User Computing Entity

FIG. 5 provides an illustrative schematic representative of an exampleuser computing entity 10 that can be used in conjunction withembodiments of the present invention. In various embodiments, a usercomputing entity 10 is configured to allow a user to provide input tothe quantum computer 30 (e.g., via a user interface of the usercomputing entity 10) and receive, view, and/or the like output from thequantum computer 30.

As shown in FIG. 5 , a user computing entity 10 can include an antenna412, a transmitter 404 (e.g., radio), a receiver 406 (e.g., radio), anda processing element 408 that provides signals to and receives signalsfrom the transmitter 404 and receiver 406, respectively. The signalsprovided to and received from the transmitter 404 and the receiver 406,respectively, may include signaling information/data in accordance withan air interface standard of applicable wireless systems to communicatewith various entities, such as a controller 500 of a quantum computer30, and/or the like. In this regard, the user computing entity 10 may becapable of operating with one or more air interface standards,communication protocols, modulation types, and access types. Moreparticularly, the user computing entity 10 may operate in accordancewith any of a number of wireless communication standards and protocols.In a particular embodiment, the user computing device 10 may operate inaccordance with multiple wireless communication standards and protocols,such as general packet radio service (GPRS), Universal MobileTelecommunications System (UMTS), Code Division Multiple Access 2000(CDMA2000), CDMA2000 1× (1×RTT), Wideband Code Division Multiple Access(WCDMA), Global System for Mobile Communications (GSM), Enhanced Datarates for GSM Evolution (EDGE), Time Division-Synchronous Code DivisionMultiple Access (TD-SCDMA), Long Term Evolution (LTE), Evolved UniversalTerrestrial Radio Access Network (E-UTRAN), Evolution-Data Optimized(EVDO), High Speed Packet Access (HSPA), High-Speed Downlink PacketAccess (HSDPA), IEEE 802.11 (Wi-Fi), Wi-Fi Direct, 802.16 (WiMAX), ultrawideband (UWB), infrared (IR) protocols, near field communication (NFC)protocols, Wibree, Bluetooth protocols, wireless universal serial bus(USB) protocols, and/or any other wireless protocol.

Via these communication standards and protocols, the user computingentity 10 can communicate with various other entities using conceptssuch as Unstructured Supplementary Service information/data (USSD),Short Message Service (SMS), Multimedia Messaging Service (MMS),Dual-Tone Multi-Frequency Signaling (DTMF), and/or Subscriber IdentityModule Dialer (SIM dialer). The user computing entity 10 can alsodownload changes, add-ons, and updates, for instance, to its firmware,software (e.g., including executable instructions, applications, programmodules), and operating system.

According to one embodiment, the user computing entity 10 may includelocation determining aspects, devices, modules, functionalities, and/orsimilar words used herein interchangeably. For example, the usercomputing entity 10 may include outdoor positioning aspects, such as alocation module adapted to acquire, for instance, latitude, longitude,altitude, geocode, course, direction, heading, speed, UTC, date, and/orvarious other information/data. In one embodiment, the location modulecan acquire data, sometimes known as ephemeris data, by identifying thenumber of satellites in view and the relative positions of thosesatellites. The satellites may be a variety of different satellites,including LEO satellite systems, DOD satellite systems, the EuropeanUnion Galileo positioning systems, the Chinese Compass navigationsystems, Indian Regional Navigational satellite systems, and/or thelike. Alternatively, the location information/data may be determined bytriangulating the user computing entity's 10 position in connection witha variety of other systems, including cellular towers, Wi-Fi accesspoints, and/or the like. Similarly, the user computing entity 10 mayinclude indoor positioning aspects, such as a location module adapted toacquire, for example, latitude, longitude, altitude, geocode, course,direction, heading, speed, time, date, and/or various otherinformation/data. Some of the indoor aspects may use various position orlocation technologies including RFID tags, indoor beacons ortransmitters, Wi-Fi access points, cellular towers, nearby computingdevices (e.g., smartphones, laptops) and/or the like. For instance, suchtechnologies may include iBeacons, Gimbal proximity beacons, BLEtransmitters, Near Field Communication (NFC) transmitters, and/or thelike. These indoor positioning aspects can be used in a variety ofsettings to determine the location of someone or something to withininches or centimeters.

The user computing entity 10 may also comprise a user interface devicecomprising one or more user input/output interfaces (e.g., a display 416and/or speaker/speaker driver coupled to a processing element 408 and atouch screen, keyboard, mouse, and/or microphone coupled to a processingelement 408). For instance, the user output interface may be configuredto provide an application, browser, user interface, interface,dashboard, screen, webpage, page, and/or similar words used hereininterchangeably executing on and/or accessible via the user computingentity 10 to cause display or audible presentation of information/dataand for user interaction therewith via one or more user inputinterfaces. The user input interface can comprise any of a number ofdevices allowing the user computing entity 10 to receive data, such as akeypad 418 (hard or soft), a touch display, voice/speech or motioninterfaces, scanners, readers, or other input device. In embodimentsincluding a keypad 418, the keypad 418 can include (or cause display of)the conventional numeric (0-9) and related keys (#, *), and other keysused for operating the user computing entity 10 and may include a fullset of alphabetic keys or set of keys that may be activated to provide afull set of alphanumeric keys. In addition to providing input, the userinput interface can be used, for example, to activate or deactivatecertain functions, such as screen savers and/or sleep modes. Throughsuch inputs the user computing entity 10 can collect information/data,user interaction/input, and/or the like.

The user computing entity 10 can also include volatile storage or memory422 and/or non-volatile storage or memory 424, which can be embeddedand/or may be removable. For instance, the non-volatile memory may beROM, PROM, EPROM, EEPROM, flash memory, MMCs, SD memory cards, MemorySticks, CBRAM, PRAM, FeRAM, RRAM, SONOS, racetrack memory, and/or thelike. The volatile memory may be RAM, DRAM, SRAM, FPM DRAM, EDO DRAM,SDRAM, DDR SDRAM, DDR2 SDRAM, DDR3 SDRAM, RDRAM, RIMM, DIMM, SIMM, VRAM,cache memory, register memory, and/or the like. The volatile andnon-volatile storage or memory can store databases, database instances,database management system entities, data, applications, programs,program modules, scripts, source code, object code, byte code, compiledcode, interpreted code, machine code, executable instructions, and/orthe like to implement the functions of the user computing entity 10.

In example embodiments, the user computing entity 10 may be incommunication with other user computing entities 10 and/or a controller500 of a quantum computer.

VII. Exemplary Quantum Computer

As shown in FIG. 6 , in various embodiments, a quantum computer 30comprises a controller 30 and one or more qubit management systems 550.For example, the one or more qubit management systems 550 may comprisethermal control systems (e.g., cryogenic cooling systems), vacuumsystems (e.g., pressure control systems), qubit confinement systems(e.g., an ion trap and voltage sources connected to the ion trap in thecase of a trapped ion quantum computer), one or more gate systems (e.g.,lasers and corresponding optics in the case of a trapped ion quantumcomputer), measurement systems (e.g., including optics, photodetectors,and/or the like in the case of a trapped ion quantum computer), and/orthe like. The controller 30 is configured and/or programmed to cause theone or more qubit management systems 550 to manipulate and/or evolve theone or more qubits in accordance with a quantum circuit enabling thequantum computer 30 to perform calculations, simulations, generatemodels, and/or the like. In various embodiments, the qubit managementsystems 550 are configured to control, contain, manipulate, manage,and/or cause the controlled evolution of one or more physical qubits 555of the quantum computer 30.

In various embodiments, the controller 500 may comprise variouscontroller elements including processing devices 505, memory 510, drivercontroller elements t15, a communication interface 520, analog-digitalconverter elements 525, and/or the like. For example, the processingdevices 505 may comprise programmable logic devices (CPLDs),microprocessors, coprocessing entities, application-specificinstruction-set processors (ASIPs), integrated circuits, applicationspecific integrated circuits (ASICs), field programmable gate arrays(FPGAs), programmable logic arrays (PLAs), hardware accelerators, otherprocessing devices and/or circuitry, controllers, and/or the like. Theterm circuitry may refer to an entirely hardware embodiment or acombination of hardware and computer program products. In an exampleembodiment, the processing device 505 of the controller 500 comprises aclock and/or is in communication with a clock. For example, the memory510 may comprise non-transitory memory such as volatile and/ornon-volatile memory storage such as one or more of as hard disks, ROM,PROM, EPROM, EEPROM, flash memory, MMCs, SD memory cards, Memory Sticks,CBRAM, PRAM, FeRAM, RRAM, SONOS, racetrack memory, RAM, DRAM, SRAM, FPMDRAM, EDO DRAM, SDRAM, DDR SDRAM, DDR2 SDRAM, DDR3 SDRAM, RDRAM, RIMM,DIMM, SIMM, VRAM, cache memory, register memory, and/or the like. Invarious embodiments, the memory 510 may store qubit recordscorresponding the qubits of quantum computer (e.g., in a qubit recorddata store, qubit record database, qubit record table, and/or the like),a calibration table, an executable queue, computer program code (e.g.,in a one or more computer languages, specialized controller language(s),and/or the like), and/or the like. In an example embodiment, executionof at least a portion of the computer program code stored in the memory510 (e.g., by a processing device 505) causes the controller 500 toperform one or more steps, operations, processes, procedures and/or thelike described herein for receiving a quantum circuit, executing aquantum circuit (e.g., slice by slice), and providing the results ofexecuting the quantum circuit.

In various embodiments, the driver controller elements 515 may includeone or more drivers and/or controller elements each configured tocontrol one or more drivers. In various embodiments, the drivercontroller elements 515 may comprise drivers and/or driver controllers.For example, the driver controllers may be configured to cause one ormore corresponding driver to be operated in accordance with executableinstructions, commands, and/or the like scheduled and executed by thecontroller 500 (e.g., by the processing device 505). In variousembodiments, the driver controller elements 515 may enable thecontroller 500 to operate the one or more qubit management systems 550to manipulate, manage, and/or evolve one or more physical qubits 555 ofthe quantum computer in accordance with a quantum circuit 100. Invarious embodiments, the drivers may be laser drivers; vacuum componentdrivers; drivers for controlling the flow of current and/or voltageapplied to DC, RF, and/or other electrodes used for maintaining and/orcontrolling, managing, and/or evolving the physical qubits 555;cryogenic and/or vacuum system component drivers; and/or the like. Invarious embodiments, the controller 500 comprises means forcommunicating and/or receiving signals from one or more optical receivercomponents such as cameras, MEMS cameras, CCD cameras, photodiodes,photomultiplier tubes, and/or the like. For example, the controller 500may comprise one or more analog-digital converter elements 525configured to receive signals from one or more optical receivercomponents, calibration sensors, and/or the like. In variousembodiments, the controller 500 may comprise a communication interface520 for interfacing and/or communicating with a user computing entity10. For example, the controller 500 may comprise a communicationinterface 520 for receiving executable instructions, command sets,and/or the like from the user computing entity 10 and providing outputreceived from the quantum computer 30 (e.g., from an optical collectionsystem) and/or the result of a processing the output to the usercomputing entity 10. In various embodiments, the user computing entity10 and the controller 500 may communicate via a direct wired and/orwireless connection and/or one or more wired and/or wireless networks.

As will be appreciated, one or more of the controller's 500 componentsmay be located remotely from other controller 500 components, such as ina distributed system. Furthermore, one or more of the components may becombined and additional components performing functions described hereinmay be included in the controller 500. Thus, the controller 500 can beadapted to accommodate a variety of needs and circumstances. Forexample, though described as a single computing entity, the controller30 may be a distributed system and/or comprise multiple computingentities, in an example embodiment. For example, in one exampleembodiment, a controller 500 may comprise a server and custom builthardware components configured for driving and/or controlling theoperation of the one or more qubit management systems 550.

CONCLUSION

Many modifications and other embodiments of the invention set forthherein will come to mind to one skilled in the art to which theinvention pertains having the benefit of the teachings presented in theforegoing descriptions and the associated drawings. Therefore, it is tobe understood that the invention is not to be limited to the specificembodiments disclosed and that modifications and other embodiments areintended to be included within the scope of the appended claims.Although specific terms are employed herein, they are used in a genericand descriptive sense only and not for purposes of limitation.

That which is claimed:
 1. A method for generating a quantum circuit, themethod comprising: defining a plurality of system qubit wires andinteractions therebetween configured for performing a quantum algorithm;identifying a past causal cone of a first system qubit wire of theplurality of system qubit wires; defining a first slice containing thepast causal cone of the first system qubit wire; identifying a secondcausal cone of a second system qubit wire of the plurality of systemqubit wires; and defining a second slice containing a portion of thesecond causal cone that is not within the first slice.
 2. The method ofclaim 1, wherein the quantum circuit is configured such that each gateof the first slice is performed prior to beginning to perform the secondslice.
 3. The method of claim 1, wherein the quantum circuit isconfigured such that executing an i-th slice of the quantum circuitcomprises executing all gates for which incoming and outgoing wires liewithin the i-th slice to propagate the system qubits forward in adimension.
 4. The method of claim 3, wherein the quantum circuitcomprises at least one ancilla wire and the quantum circuit isconfigured such that an i-th slice of the quantum circuit comprisesinteracting one or more system qubits at a bottom of the i-th slice withat least one ancilla qubit via unitary gates in order to introduceinitial correlations between the one or more system qubits at the bottomof the i-th slice and system qubits at the bottom of one or more otherslices.
 5. The method of claim 1, wherein the quantum circuit encodesinteractions governed by a Hamiltonian characterized by localinteractions.
 6. The method of claim 1, wherein each system qubit wirecorresponds to a degree of freedom associated with a section of aphysical domain being simulated.
 7. The method of claim 6, wherein ani-th slice of the quantum circuit is configured to, upon execution by aquantum processor, evolve the degree of freedom in accordance with anoperator.
 8. The method of claim 7, wherein the operator is aHamiltonian.
 9. The method of claim 6, wherein the physical domain isone of a one dimensional, two dimensional, or three dimensional physicaldomain.
 10. The method of claim 6, wherein the quantum circuit simulatesthe dynamics of the evolution of quantum states defined on a latticerepresenting the physical domain.
 11. The method of claim 6, furthercomprising causing the quantum circuit to be configured to causemeasurement of at least one physical qubit of the plurality of qubits todetermine a value corresponding to at least one degree of freedom withinthe physical domain.
 12. The method of claim 1, wherein at least onesystem qubit wire of the quantum circuit extends through multiple slicesof quantum circuit.
 13. A computing entity comprising at least oneprocessor and a memory storing computer-executable instructions, thecomputer executable-instructions configured, when executed by the atleast one processor, to cause the apparatus to at least: generate aquantum circuit divided into slices by: defining a plurality of systemqubit wires and interactions therebetween configured for performing aquantum algorithm; identifying a past causal cone of a first systemqubit wire of the plurality of system qubit wires; defining a firstslice containing the past causal cone of the first system qubit wire;identifying a second causal cone of a second system qubit wire of theplurality of system qubit wires; and defining a second slice containinga portion of the second causal cone that is not within the first slice.14. The computing entity of claim 13, wherein the quantum circuit isconfigured such that each gate of the first slice is performed prior tobeginning to perform the second slice.
 15. The computing entity of claim13, wherein the quantum circuit is configured such that executing ani-th slice of the quantum circuit comprises executing all gates forwhich incoming and outgoing wires lie within the i-th slice to propagatethe system qubits forward in a dimension.
 16. The computing entity ofclaim 15, wherein the quantum circuit comprises at least one ancillawire and the quantum circuit is configured such that an i-th slice ofthe quantum circuit comprises interacting one or more system qubits at abottom of the i-th slice with at least one ancilla qubit via unitarygates in order to introduce initial correlations between the one or moresystem qubits at the bottom of the i-th slice and system qubits at thebottom of one or more other slices.
 17. The computing entity of claim13, wherein the quantum circuit encodes interactions governed by anoperator characterized by local interactions.
 18. The computing entityof claim 13, wherein each system qubit wire corresponds to a degree offreedom associated with a section of a physical domain being simulated.19. The computing entity of claim 18, wherein an i-th slice of thequantum circuit is configured to, upon execution by a quantum processor,evolve the degree of freedom in accordance with an operator.
 20. Thecomputing entity of claim 18, wherein the quantum circuit simulates thedynamics of the evolution of quantum states defined on a latticerepresenting the physical domain.